Controlled fusion in a field reversed configuration and direct energy conversion

ABSTRACT

A system and apparatus for controlled fusion in a field reversed configuration (FRC) magnetic topology and conversion of fusion product energies directly to electric power. Preferably, plasma ions are magnetically confined in the FRC while plasma electrons are electrostatically confined in a deep energy well, created by tuning an externally applied magnetic field. In this configuration, ions and electrons may have adequate density and temperature so that upon collisions they are fused together by the nuclear force, thus forming fusion products that emerge in the form of an annular beam. Energy is removed from the fusion product ions as they spiral past electrodes of an inverse cyclotron converter. Advantageously, the fusion fuel plasmas that can be used with the present confinement and energy conversion system include advanced (aneutronic) fuels.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of U.S. application Ser. No.10/076,793, filed Feb. 14, 2002, which claims the benefit of U.S.provisional application serial No. 60/277,374, filed Mar. 19, 2001, andU.S. provisional application serial No. 60/297,086, filed on Jun. 8,2001, which applications are fully incorporated herein by reference.

FIELD OF THE INVENTION

[0002] The invention relates generally to the field of plasma physics,and, in particular, to methods and apparati for confining plasma toenable nuclear fusion and for converting energy from fusion productsinto electricity.

BACKGROUND OF THE INVENTION

[0003] Fusion is the process by which two light nuclei combine to form aheavier one. The fusion process releases a tremendous amount of energyin the form of fast moving particles. Because atomic nuclei arepositively charged—due to the protons contained therein—there is arepulsive electrostatic, or Coulomb, force between them. For two nucleito fuse, this repulsive barrier must be overcome, which occurs when twonuclei are brought close enough together where the short-range nuclearforces, become strong enough to overcome the Coulomb force and fuse thenuclei. The energy necessary for the nuclei to overcome the Coulombbarrier is provided by their thermal energies, which must be very high.For example, the fusion rate can be appreciable if the temperature is atleast of the order of 10⁴ eV—corresponding roughly to 100 milliondegrees Kelvin. The rate of a fusion reaction is a function of thetemperature, and it is characterized by a quantity called reactivity.The reactivity of a D-T reaction, for example, has a broad peak between30 keV and 100 keV.

[0004] Typical fusion reactions include:

D+D→He³(0.8 MeV)+n(2.5 MeV),

D+T→α(3.6 MeV)+n(14.1 MeV),

D+He³→α(3.7 MeV)+p(14.7 MeV), and

p+B¹¹→3α(8.7 MeV),

[0005] where D indicates deuterium, T indicates tritium, α indicates ahelium nucleus, n indicates a neutron, p indicates a proton, Heindicates helium, and B¹¹ indicates Boron-11. The numbers in parenthesesin each equation indicate the kinetic energy of the fusion products.

[0006] The first two reactions listed above—the D-D and D-Treactions—are neutronic, which means that most of the energy of theirfusion products is carried by fast neutrons. The disadvantages ofneutronic reactions are that (1) the flux of fast neutrons creates manyproblems, including structural damage of the reactor walls and highlevels of radioactivity for most construction materials; and (2) theenergy of fast neutrons is collected by converting their thermal energyto electric energy, which is very inefficient (less than 30%). Theadvantages of neutronic reactions are that (1) their reactivity peaks ata relatively low temperature; and (2) their losses due to radiation arerelatively low because the atomic numbers of deuterium and tritium are1.

[0007] The reactants in the other two equations—D-He3 and p-B¹¹—arecalled advanced fuels. Instead of producing fast neutrons, as in theneutronic reactions, their fusion products are charged particles. Oneadvantage of the advanced fuels is that they create much fewer neutronsand therefore suffer less from the disadvantages associated with them.In the case of D-He³, some fast neutrons are produced by secondaryreactions, but these neutrons account for only about 10 percent of theenergy of the fusion products. The p-B¹¹ reaction is free of fastneutrons, although it does produce some slow neutrons that result fromsecondary reactions but create much fewer problems. Another advantage ofthe advanced fuels is that their fusion products comprise chargedparticles whose kinetic energy may be directly convertible toelectricity. With an appropriate direct energy conversion process, theenergy of advanced fuel fusion products may be collected with a highefficiency, possibly in excess of 90 percent.

[0008] The advanced fuels have disadvantages, too. For example, theatomic numbers of the advanced fuels are higher (2 for He³ and 5 forB¹¹). Therefore, their radiation losses are greater than in theneutronic reactions. Also, it is much more difficult to cause theadvanced fuels to fuse. Their peak reactivities occur at much highertemperatures and do not reach as high as the reactivity for D-T. Causinga fusion reaction with the advanced fuels thus requires that they bebrought to a higher energy state where their reactivity is significant.Accordingly, the advanced fuels must be contained for a longer timeperiod wherein they can be brought to appropriate fusion conditions.

[0009] The containment time for a plasma is Δt=r²/D, where r is aminimum plasma dimension and D is a diffusion coefficient. The classicalvalue of the diffusion coefficient is D_(c)=a_(i) ²/τ_(ie), where a_(i)is the ion gyroradius and τ_(ie) is the ion-electron collision time.Diffusion according to the classical diffusion coefficient is calledclassical transport. The Bohm diffusion coefficient, attributed toshort-wavelength instabilities, is D_(B)=({fraction (1/16)})Ω_(i)²Ω_(i), where Ω_(i) is the ion gyrofrequency. Diffusion according tothis relationship is called anomalous transport. For fusion conditions,D_(B)/D_(c)=({fraction (1/16)})Ω_(i)τ_(ie)≅10⁸, anomalous transportresults in a much shorter containment time than does classicaltransport. This relation determines how large a plasma must be in afusion reactor, by the requirement that the containment time for a givenamount of plasma must be longer than the time for the plasma to have anuclear fusion reaction. Therefore, classical transport condition ismore desirable in a fusion reactor, allowing for smaller initialplasmas.

[0010] In early experiments with toroidal confinement of plasma, acontainment time of Δt≅r²/D_(B) was observed. Progress in the last 40years has increased the containment time to Δt≅1000 r²/D_(B). Oneexisting fusion reactor concept is the Tokamak. The magnetic field of aTokamak 68 and a typical particle orbit 66 are illustrated in FIG. 5.For the past 30 years, fusion efforts have been focussed on the Tokamakreactor using a D-T fuel. These efforts have culminated in theInternational Thermonuclear Experimental Reactor (ITER), illustrated inFIG. 7. Recent experiments with Tokamaks suggest that classicaltransport, Δt≅r²/D_(c), is possible, in which case the minimum plasmadimension can be reduced from meters to centimeters. These experimentsinvolved the injection of energetic beams (50 to 100 keV), to heat theplasma to temperatures of 10 to 30 keV. See W. Heidbrink & G. J. Sadler,34 Nuclear Fusion 535 (1994). The energetic beam ions in theseexperiments were observed to slow down and diffuse classically while thethermal plasma continued to diffuse anomalously fast. The reason forthis is that the energetic beam ions have a large gyroradius and, assuch, are insensitive to fluctuations with wavelengths-shorter than theion gyroradius (λ<a_(i)). The short-wavelength fluctuations tend toaverage over a cycle and thus cancel. Electrons, however, have a muchsmaller gyroradius, so they respond to the fluctuations and transportanomalously.

[0011] Because of anomalous transport, the minimum dimension of theplasma must be at least 2.8 meters. Due to this dimension, the ITER wascreated 30 meters high and 30 meters in diameter. This is the smallestD-T Tokamak-type reactor that is feasible. For advanced fuels, such asD-He³ and p-B¹¹, the Tokamak-type reactor would have to be much largerbecause the time for a fuel ion to have a nuclear reaction is muchlonger. A Tokamak reactor using D-T fuel has the additional problem thatmost of the energy of the fusion products energy is carried by 14 MeVneutrons, which cause radiation damage and induce reactivity in almostall construction materials due to the neutron flux. In addition, theconversion of their energy into electricity must be by a thermalprocess, which is not more than 30% efficient.

[0012] Another proposed reactor configuration is a colliding beamreactor. In a colliding beam reactor, a background plasma is bombardedby beams of ions. The beams comprise ions with an energy that is muchlarger than the thermal plasma. Producing useful fusion reactions inthis type of reactor has been infeasible because the background plasmaslows down the ion beams. Various proposals have been made to reducethis problem and maximize the number of nuclear reactions.

[0013] For example, U.S. Pat. No. 4,065,351 to Jassby et al. discloses amethod of producing counterstreaming colliding beams of deuterons andtritons in a toroidal confinement system. In U.S. Pat. No. 4,057,462 toJassby et al., electromagnetic energy is injected to counteract theeffects of bulk equilibrium plasma drag on one of the ion species. Thetoroidal confinement system is identified as a Tokamak. In U.S. Pat. No.4,894,199 to Rostoker, beams of deuterium and tritium are injected andtrapped with the same average velocity in a Tokamak, mirror, or fieldreversed configuration. There is a low density cool background plasmafor the sole purpose of trapping the beams. The beams react because theyhave a high temperature, and slowing down is mainly caused by electronsthat accompany the injected ions. The electrons are heated by the ionsin which case the slowing down is minimal.

[0014] In none of these devices, however, does an equilibrium electricfield play any part. Further, there is no attempt to reduce, or evenconsider, anomalous transport.

[0015] Other patents consider electrostatic confinement of ions and, insome cases, magnetic confinement of electrons. These include U.S. Pat.No. 3,258,402 to Farnsworth and U.S. Pat. No. 3,386,883 to Farnsworth,which disclose electrostatic confinement of ions and inertialconfinement of electrons; U.S. Pat. No. 3,530,036 to Hirsch et al. andU.S. Pat. No. 3,530,497 to Hirsch et al. are similar to Farnsworth; U.S.Pat. No. 4,233,537 to Limpaecher, which discloses electrostaticconfinement of ions and magnetic confinement of electrons withmulti-pole cusp reflecting walls; and U.S. Pat. No. 4,826,646 toBussard, which is similar to Limpaecher and involves point cusps. Noneof these patents consider electrostatic confinement of electrons andmagnetic confinement of ions. Although there have been many researchprojects on electrostatic confinement of ions, none of them havesucceeded in establishing the required electrostatic fields when theions have the required density for a fusion reactor. Lastly, none of thepatents cited above discuss a field reversed configuration magnetictopology.

[0016] The field reversed configuration (FRC) was discoveredaccidentally around 1960 at the Naval Research Laboratory during thetapinch experiments. A typical FRC topology, wherein the internal magneticfield reverses direction, is illustrated in FIG. 8 and FIG. 10, andparticle orbits in a FRC are shown in FIG. 11 and FIG. 14. Regarding theFRC, many research programs have been supported in the United States andJapan. There is a comprehensive review paper on the theory andexperiments of FRC research from 1960-1988. See M. Tuszewski, 28 NuclearFusion 2033, (1988). A white paper on FRC development describes theresearch in 1996 and recommendations for future research. See L. C.Steinhauer et al., 30 Fusion Technology 116 (1996). To this date, in FRCexperiments the FRC has been formed with the theta pinch method. Aconsequence of this formation method is that the ions and electrons eachcarry half the current, which results in a negligible electrostaticfield in the plasma and no electrostatic confinement. The ions andelectrons in these FRCs were contained magnetically. In almost all FRCexperiments, anomalous transport has been assumed. See, e.g., Tuszewski,beginning of section 1.5.2, at page 2072.

[0017] Thus, it is desirable to provide a fusion system having acontainment system that tends to substantially reduce or eliminateanomalous transport of ions and electrons and an energy conversionsystem that converts the energy of fusion products to electricity withhigh efficiency.

SUMMARY OF THE INVENTION

[0018] The present invention is directed to a system that facilitatescontrolled fusion in a magnetic field having a field-reversed topologyand the direct conversion of fusion product energies to electric power.The system, referred to herein as a plasma-electric power generation(PEG) system, preferably includes a fusion reactor having a containmentsystem that tends to substantially reduce or eliminate anomaloustransport of ions and electrons. In addition, the PEG system includes anenergy conversion system coupled to the reactor that directly convertsfusion product energies to electricity with high efficiency.

[0019] In one innovative aspect of the present invention, anomaloustransport for both ions and electrons tends to be substantially reducedor eliminated. The anomalous transport of ions tends to be avoided bymagnetically confining the ions in a magnetic field of field reversedconfiguration (FRC). For electrons, the anomalous transport of energy isavoided by tuning an externally applied magnetic field to develop astrong electric field, which confines the electrons electrostatically ina deep potential well. As a result, fusion fuel plasmas that can be usedwith the present confinement apparatus and process are not limited toneutronic fuels, but also advantageously include advanced or aneutronicfuels. For aneutronic fuels, fusion reaction energy is almost entirelyin the form of charged particles, i.e., energetic ions, that can bemanipulated in a magnetic field and, depending on the fuel, cause littleor no radioactivity.

[0020] In another innovative aspect of the present invention, a directenergy conversion system is used to convert the kinetic energy of thefusion products directly into electric power by slowing down the chargedparticles through an electromagnetic field. Advantageously, the directenergy conversion system of the present invention has the efficiencies,particle-energy tolerances and electronic ability to convert thefrequency and phase of the fusion output power of about 5 MHz to matchthe frequency of an external 60 Hertz power grid.

[0021] In a preferred embodiment, the fusion reactor's plasmacontainment system comprises a chamber, a magnetic field generator forapplying a magnetic field in a direction substantially along a principleaxis, and an annular plasma layer that comprises a circulating beam ofions. Ions of the annular plasma beam layer are substantially containedwithin the chamber magnetically in orbits and the electrons aresubstantially contained in an electrostatic energy well. In one aspectof one preferred embodiment a magnetic field generator comprises acurrent coil. Preferably, the system further comprises mirror coils nearthe ends of the chamber that increase the magnitude of the appliedmagnetic field at the ends of the chamber. The system may also comprisea beam injector for injecting a neutralized ion beam into the appliedmagnetic field, wherein the beam enters an orbit due to the force causedby the applied magnetic field. In another aspect of the preferredembodiments, the system forms a magnetic field having a topology of afield reversed configuration.

[0022] In another preferred embodiment, the energy conversion systemcomprises inverse cyclotron converters (ICC) coupled to opposing ends ofthe fusion reactor. The ICC have a hollow cylinder-like geometry formedfrom multiple, preferably four or more equal, semi-cylindricalelectrodes with small, straight gaps extending there between. Inoperation, an oscillating potential is applied to the electrodes in analternating fashion. The electric field E within the ICC has amulti-pole structure and vanishes on the symmetry axes and increaseslinearly with radius; the peak value being at the gap.

[0023] In addition, the ICC includes a magnetic field generator forapplying a uniform uni-directional magnetic field in a directionsubstantially opposite to that of the fusion reactor's containmentsystem. At an end furthest from the fusion reactor power core the ICCincludes an ion collector. In between the power core and the ICC is asymmetric magnetic cusp wherein the magnetic field of the containmentsystem merges with the magnetic field of the ICC. An annular shapedelectron collector is positioned about the magnetic cusp andelectrically coupled to the ion collector.

[0024] In yet another preferred embodiment, product nuclei andcharge-neutralizing electrons emerge as annular beams from both ends ofthe reactor power core with a density at which the magnetic cuspseparates electrons and ions due to their energy differences. Theelectrons follow magnetic field lines to the electron collector and theions pass through the cusp where the ion trajectories are modified tofollow a substantially helical path along the length of the ICC. Energyis removed from the ions as they spiral past the electrodes, which areconnected to a resonant circuit. The loss of perpendicular energy tendsto be greatest for the highest energy ions that initially circulateclose to the electrodes, where the electric field is strongest.

[0025] Other aspects and features of the present invention will becomeapparent from consideration of the following description taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Preferred embodiments are illustrated by way of example, and notby way of limitation, in the figures of the accompanying drawings, inwhich like reference numerals refer to like components.

[0027]FIG. 1 shows an exemplary confinement chamber of the presentinvention.

[0028]FIG. 2 shows the magnetic field of a FRC.

[0029]FIGS. 3A and 3B show, respectively, the diamagnetic and thecounterdiamagnetic direction in a FRC.

[0030]FIG. 4 shows the colliding beam system of the present invention.

[0031]FIG. 5 shows a betatron orbit.

[0032]FIGS. 6A and 6B show, respectively, the magnetic field and thedirection of the gradient drift in a FRC.

[0033]FIGS. 7A and 7B show, respectively, the electric field and thedirection of the {right arrow over (E)}×{right arrow over (B)} drift ina FRC.

[0034]FIGS. 8A, 8B and 8C show ion drift orbits.

[0035]FIGS. 9A and 9B show the Lorentz force at the ends of a FRC.

[0036]FIGS. 10A and 10B show the tuning of the electric field and theelectric potential in the colliding beam system.

[0037]FIG. 11 shows a Maxwell distribution.

[0038]FIGS. 12A and 12B show transitions from betatron orbits to driftorbits due to large-angle, ion-ion collisions.

[0039]FIG. 13 show A, B, C and D betatron orbits when small-angle,electron-ion collisions are considered.

[0040]FIG. 14 shows a neutralized ion beam as it is electricallypolarized before entering a confining chamber.

[0041]FIG. 15 is a head-on view of a neutralized ion beam as it contactsplasma in a confining chamber.

[0042]FIG. 16 is a side view schematic of a confining chamber accordingto a preferred embodiment of a start-up procedure.

[0043]FIG. 17 is a side view schematic of a confining chamber accordingto another preferred embodiment of a start-up procedure.

[0044]FIG. 18 shows traces of B-dot probe indicating the formation of aFRC.

[0045]FIG. 19A shows a partial plasma-electric power generation systemcomprising a colliding beam fusion reactor coupled to an inversecyclotron direct energy converter.

[0046]FIG. 19B shows an end view of the inverse cyclotron converter inFIG. 19A.

[0047]FIG. 19C shows an orbit of an ion in the inverse cyclotronconverter.

[0048]FIG. 20A shows a partial plasma electric power generation systemcomprising a colliding beam fusion reactor coupled to an alternateembodiment of the inverse cyclotron converter.

[0049]FIG. 20B shows an end view of the inverse cyclotron converter inFIG. 20A.

[0050]FIG. 21A shows a particle orbit inside a conventional cyclotron.

[0051]FIG. 21B shows an oscillating electric field.

[0052]FIG. 21C shows the changing energy of an accelerating particle.

[0053]FIG. 22 shows an azimuthal electric field at gaps between theelectrodes of the ICC that is experienced by an ion with angularvelocity.

[0054]FIG. 23 shows a focusing quadrupole doublet lens.

[0055]FIGS. 24A and 24B show auxiliary magnetic-field-coil system.

[0056]FIG. 25 shows a 100 MW reactor.

[0057]FIG. 26 shows reactor support equipment.

[0058]FIG. 27 shows a plasma-thrust propulsion system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0059] As illustrated in the figures, a plasma-electric power generationsystem of the present invention preferably includes a colliding beamfusion reactor coupled to a direct energy conversion system. As alludedto above, an ideal fusion reactor solves the problem of anomaloustransport for both ions and electrons. The solution to the problem ofanomalous transport found herein makes use of a containment system witha magnetic field having a field reversed configuration (FRC). Theanomalous transport of ions is avoided by magnetic confinement in theFRC in such a way that the majority of the ions have large,non-adiabatic orbits, making them insensitive to short-wavelengthfluctuations that cause anomalous transport of adiabatic ions. Inparticular, the existence of a region in the FRC where the magneticfield vanishes makes it possible to have a plasma comprising a majorityof non-adiabatic ions. For electrons, the anomalous transport of energyis avoided by tuning the externally applied magnetic field to develop astrong electric field, which confines them electrostatically in a deeppotential well.

[0060] Fusion fuel plasmas that can be used with the present confinementapparatus and process are not limited to neutronic fuels such as D-D(Deuterium-Deuterium) or D-T (Deuterium-Tritium), but alsoadvantageously include advanced or aneutronic fuels such as D-He³(Deuterium-helium-3) or p-B¹¹ (hydrogen-Boron-11). (For a discussion ofadvanced fuels, see R. Feldbacher & M. Heindler, Nuclear Instruments andMethods in Physics Research, A271(1988)JJ-64 (North Holland Amsterdam).)For such aneutronic fuels, the fusion reaction energy is almost entirelyin the form of charged particles, i.e., energetic ions, that can bemanipulated in a magnetic field and, depending on the fuel, cause littleor no radioactivity. The D-He³ reaction produces an H ion and an He⁴ ionwith 18.2 MeV energy while the p-B¹¹ reaction produces three He⁴ ionsand 8.7 MeV energy. Based on theoretical modeling for a fusion deviceutilizing aneutronic fuels, the output energy conversion efficiency maybe as high as about 90%, as described by K. Yoshikawa, T. Noma and Y.Yamamoto in Fusion Technology, 19, 870 (1991), for example. Suchefficiencies dramatically advance the prospects for aneutronic fusion,in a scalable (1-1000 MW), compact, low-cost configuration.

[0061] In a direct energy conversion process of the present invention,the charged particles of fusion products can be slowed down and theirkinetic energy converted directly to electricity. Advantageously, thedirect energy conversion system of the present invention has theefficiencies, particle-energy tolerances and electronic ability toconvert the frequency and phase of the fusion output power of about 5MHz to match the frequency and phase of an external 60 Hertz power grid.

[0062] Fusion Containment System

[0063]FIG. 1 illustrates a preferred embodiment of a containment system300 according to the present invention. The containment system 300comprises a chamber wall 305 that defines therein a confining chamber310. Preferably, the chamber 310 is cylindrical in shape, with principleaxis 315 along the center of the chamber 310. For application of thiscontainment system 300 to a fusion reactor, it is necessary to create avacuum or near vacuum inside the chamber 310. Concentric with theprinciple axis 315 is a betatron flux coil 320, located within thechamber 310. The betatron flux coil 320 comprises an electrical currentcarrying medium adapted to direct current around a long coil, as shown,which preferably comprises parallel windings of multiple separate coilsand, most preferably, parallel windings of about four separate coils, toform a long coil. Persons skilled in the art will appreciate thatcurrent through the betatron coil 320 will result in a magnetic fieldinside the betatron coil 320, substantially in the direction of theprinciple axis 315.

[0064] Around the outside of the chamber wall 305 is an outer coil 325.The outer coil 325 produce a relatively constant magnetic field havingflux substantially parallel with principle axis 315. This magnetic fieldis azimuthally symmetrical. The approximation that the magnetic fielddue to the outer coil 325 is constant and parallel to axis 315 is mostvalid away from the ends of the chamber 310. At each end of the chamber310 is a mirror coil 330. The mirror coils 330 are adapted to produce anincreased magnetic field inside the chamber 310 at each end, thusbending the magnetic field lines inward at each end. (See FIGS. 8 and10.) As explained, this bending inward of the field lines helps tocontain the plasma 335 in a containment region within the chamber 310generally between the mirror coils 330 by pushing it away from the endswhere it can escape the containment system 300. The mirror coils 330 canbe adapted to produce an increased magnetic field at the ends by avariety of methods known in the art, including increasing the number ofwindings in the mirror coils 330, increasing the current through themirror coils 330, or overlapping the mirror coils 330 with the outercoil 325.

[0065] The outer coil 325 and mirror coils 330 are shown in FIG. 1implemented outside the chamber wall 305; however, they may be insidethe chamber 310. In cases where the chamber wall 305 is constructed of aconductive material such as metal, it may be advantageous to place thecoils 325, 330 inside the chamber wall 305 because the time that ittakes for the magnetic field to diffuse through the wall 305 may berelatively large and thus cause the system 300 to react sluggishly.Similarly, the chamber 310 may be of the shape of a hollow cylinder, thechamber wall 305 forming a long, annular ring. In such a case, thebetatron flux coil 320 could be implemented outside of the chamber wall305 in the center of that annular ring. Preferably, the inner wallforming the center of the annular ring may comprise a non-conductingmaterial such as glass. As will become apparent, the chamber 310 must beof sufficient size and shape to allow the circulating plasma beam orlayer 335 to rotate around the principle axis 315 at a given radius.

[0066] The chamber wall 305 may be formed of a material having a highmagnetic permeability, such as steel. In such a case, the chamber wall305, due to induced countercurrents in the material, helps to keep themagnetic flux from escaping the chamber 310, “compressing” it. If thechamber wall were to be made of a material having low magneticpermeability, such as plexiglass, another device for containing themagnetic flux would be necessary. In such a case, a series ofclosed-loop, flat metal rings could be provided. These rings, known inthe art as flux delimiters, would be provided within the outer coils 325but outside the circulating plasma beam 335. Further, these fluxdelimiters could be passive or active, wherein the active fluxdelimiters would be driven with a predetermined current to greaterfacilitate the containment of magnetic flux within the chamber 310.Alternatively, the outer coils 325 themselves could serve as fluxdelimiters.

[0067] As explained in further detail below, a circulating plasma beam335, comprising charged particles, may be contained within the chamber310 by the Lorentz force caused by the magnetic field due to the outercoil 325. As such, the ions in the plasma beam 335 are magneticallycontained in large betatron orbits about the flux lines from the outercoil 325, which are parallel to the principle axis 315. One or more beaminjection ports 340 are also provided for adding plasma ions to thecirculating plasma beam 335 in the chamber 310. In a preferredembodiment, the injector ports 340 are adapted to inject an ion beam atabout the same radial position from the principle axis 315 where thecirculating plasma beam 335 is contained (i.e., around a null surfacedescribed below). Further, the injector ports 340 are adapted to injection beams 350 (See FIG. 16) tangent to and in the direction of thebetatron orbit of the contained plasma beam 335.

[0068] Also provided are one or more background plasma sources 345 forinjecting a cloud of non-energetic plasma into the chamber 310. In apreferred embodiment, the background plasma sources 345 are adapted todirect plasma 335 toward the axial center of the chamber 310. It hasbeen found that directing the plasma this way helps to better containthe plasma 335 and leads to a higher density of plasma 335 in thecontainment region within the chamber 310.

[0069] Charged Particles in a FRC

[0070]FIG. 2 shows a magnetic field of a FRC 70. The system hascylindrical symmetry with respect to its axis 78. In the FRC, there aretwo regions of magnetic field lines: open 80 and closed 82. The surfacedividing the two regions is called the separatrix 84. The FRC forms acylindrical null surface 86 in which the magnetic field vanishes. In thecentral part 88 of the FRC the magnetic field does not changeappreciably in the axial direction. At the ends 90, the magnetic fielddoes change appreciably in the axial direction. The magnetic field alongthe center axis 78 reverses direction in the FRC, which gives rise tothe term “Reversed” in Field Reversed Configuration (FRC).

[0071] In FIG. 3A, the magnetic field outside of the null surface 94 isin a first direction 96. The magnetic field inside the null surface 94is in a second direction 98 opposite the first. If an ion moves in thedirection 100, the Lorentz force 30 acting on it points towards the nullsurface 94. This is easily appreciated by applying the right-hand rule.For particles moving in the diamagnetic direction 102, the Lorentz forcealways points toward the null surface 94. This phenomenon gives rise toa particle orbit called betatron orbit, to be described below.

[0072]FIG. 3B shows an ion moving in the counterdiamagnetic direction104. The Lorentz force in this case points away from the null surface94. This phenomenon gives rise to a type of orbit called a drift orbit,to be described below. The diamagnetic direction for ions iscounterdiamagnetic for electrons, and vice versa.

[0073]FIG. 4 shows a ring or annular layer of plasma 106 rotating in theions' diamagnetic direction 102. The ring 106 is located around the nullsurface 86. The magnetic field 108 created by the annular plasma layer106, in combination with an externally applied magnetic field 110, formsa magnetic field having the topology of a FRC (The topology is shown inFIG. 2).

[0074] The ion beam that forms the plasma layer 106 has a temperature;therefore, the velocities of the ions form a Maxwell distribution in aframe rotating at the average angular velocity of the ion beam.Collisions between ions of different velocities lead to fusionreactions. For this reason, the plasma beam layer or power core 106 iscalled a colliding beam system.

[0075]FIG. 5 shows the main type of ion orbits in a colliding beamsystem, called a betatron orbit 112. A betatron orbit 112 can beexpressed as a sine wave centered on the null circle 114. As explainedabove, the magnetic field on the null circle 114 vanishes. The plane ofthe orbit 112 is perpendicular to the axis 78 of the FRC. Ions in thisorbit 112 move in their diamagnetic direction 102 from a starting point116. An ion in a betatron orbit has two motions: an oscillation in theradial direction (perpendicular to the null circle 114), and atranslation along the null circle 114.

[0076]FIG. 6A is a graph of the magnetic field 118 in a FRC. Thehorizontal axis of the graph represents the distance in centimeters fromthe FRC axis 78. The magnetic field is in kilogauss. As the graphdepicts, the magnetic field 118 vanishes at the null circle radius 120.

[0077] As shown in FIG. 6B, a particle moving near the null circle willsee a gradient 126 of the magnetic field pointing away from the nullsurface 86. The magnetic field outside the null circle is in a firstdirection 122, while the magnetic field inside the null circle is in asecond direction 124 opposite to the first. The direction of a gradientdrift is given by the cross product {right arrow over (B)}×∇VB, where ∇Bis the gradient of the magnetic field; thus, it can be appreciated byapplying the right-hand rule that the direction of the gradient drift isin the counterdiamagnetic direction, whether the ion is outside orinside the null circle 128.

[0078]FIG. 7A is a graph of the electric field 130 in a FRC. Thehorizontal axis of the graph represents the distance in centimeters fromthe FRC axis 78. The electric field is in volts/cm. As the graphdepicts, the electric field 130 vanishes close to the null circle radius120.

[0079] As shown if FIG. 7B, the electric field for ions is deconfining;it points in directions 132, 134 away from the null surface 86. Themagnetic field, as before, is in opposite directions 122,124 inside andoutside of the null surface 86. It can be appreciated by applying theright-hand rule that the direction of the {right arrow over (E)}×{rightarrow over (B)} drift is in the diamagnetic direction 102, whether theion is outside or inside the null surface 136.

[0080]FIGS. 8A and 8B show another type of common orbit in a FRC, calleda drift orbit 138. Drift orbits 138 can be outside of the null surface114, as shown in FIG. 8A, or inside it, as shown in FIG. 8B. Driftorbits 138 rotate in the diamagnetic direction if the {right arrow over(E)}×{right arrow over (B)} drift dominates or in the counterdiamagneticdirection if the gradient drift dominates. The drift orbits 138 shown inFIGS. 8A and 8B rotate in the diamagnetic direction 102 from startingpoint 116.

[0081] A drift orbit, as shown in FIG. 8C, can be thought of as a smallcircle rolling over a relatively bigger circle. The small circle 142spins around its axis in the sense 144. It also rolls over the bigcircle 146 in the direction 102. The point 140 will trace in space apath similar to 138.

[0082]FIGS. 9A and 9B show the direction of the Lorentz force at theends of a FRC 151. In FIG. 9A, an ion is shown moving in the diamagneticdirection 102 with a velocity 148 in a magnetic field 150. It can beappreciated by applying the right-hand rule that the Lorentz force 152tends to push the ion back into the region of closed field lines. Inthis case, therefore, the Lorentz force 152 is confining for the ions.In FIG. 9B, an ion is shown moving in the counterdiamagnetic directionwith a velocity 148 in a magnetic field 150. It can be appreciated byapplying the right-hand rule that the Lorentz force 152 tends to pushthe ion into the region of open field lines. In this case, therefore,the Lorentz force 152 is deconfining for the ions.

[0083] Magnetic and Electrostatic Confinement in a FRC

[0084] A plasma layer 106 (see FIG. 4) can be formed in a FRC byinjecting energetic ion beams around the null surface 86 in thediamagnetic direction 102 of ions. (A detailed discussion of differentmethods of forming the FRC and plasma ring follows below.) In thecirculating plasma layer 106, most of the ions have betatron orbits. 112(see FIG. 5), are energetic, and are non-adiabatic; thus, they areinsensitive to short-wavelength fluctuations that cause anomaloustransport.

[0085] In a plasma layer 106 formed in a FRC and under equilibriumconditions, the conservation of momentum imposes a relation between theangular velocity of ions ω_(i) and the angular velocity of electronsω_(e). The relation is $\begin{matrix}{{\omega_{e} = {\omega_{i}\left\lbrack {1 - \frac{\omega_{i}}{\Omega_{0}}} \right\rbrack}},{{{where}\quad \Omega_{0}} = {\frac{{ZeB}_{0}}{m_{i}c}.}}} & (1)\end{matrix}$

[0086] In Eq. 1, Z is the ion atomic number, m_(i) is the ion mass, e isthe electron charge, Bo is the magnitude of the applied magnetic field,and c is the speed of light. There are three free parameters in thisrelation: the applied magnetic field B₀, the electron angular velocityω_(e), and the ion angular velocity ω_(i). If two of them are known, thethird can be determined from Eq. 1.

[0087] Because the plasma layer 106 is formed by injecting ion beamsinto the FRC, the angular velocity of ions ω_(i) is determined by theinjection kinetic energy of the beam W_(i), which is given by$\begin{matrix}{W_{i} = {{\frac{1}{2}m_{i}V_{i}^{2}} = {\frac{1}{2}{m_{i}\left( {\omega_{i}r_{o}} \right)}^{2}}}} & (2)\end{matrix}$

[0088] Here, V_(i)=ω_(i)r₀, where V_(i) is the injection velocity ofions, ω_(i) is the cyclotron frequency of ions, and r₀ is the radius ofthe null surface 86. The kinetic energy of electrons in the beam hasbeen ignored because the electron mass m_(e) is much smaller than theion mass m_(i).

[0089] For a fixed injection velocity of the beam (fixed ω_(i)), theapplied magnetic field B₀ can be tuned so that different values of ω_(e)are obtainable. As will be shown, tuning the external magnetic field B₀also gives rise to different values of the electrostatic field insidethe plasma layer. This feature of the invention is illustrated in FIGS.10A and 10B. FIG. 10A shows three plots of the electric field (involts/cm) obtained for the same injection velocity, ω_(i)=1.35×10⁷ s⁻¹,but for three different values of the applied magnetic field B₀: PlotApplied magnetic field (B₀) electron angular velocity (ω_(e)) 154 B₀ =2.77 kG ω_(e) = 0 156 B₀ = 5.15 kG ω_(e) = 0.625 × 10⁷ s⁻¹ 158 B₀ = 15.5kG ω_(e) = 1.11 × 10⁷ s⁻¹

[0090] The values of ω_(e) in the table above were determined accordingto Eq. 1. One can appreciate that ω_(e)>0 means that Ω₀>ω_(i) in Eq. 1,so that electrons rotate in their counterdiamagnetic direction. FIG. 10Bshows the electric potential (in volts) for the same set of values of B₀and ω_(e). The horizontal axis, in FIGS. 10A and 10B, represents thedistance from the FRC axis 78, shown in the graph in centimeters. Theelectric field and electric potential depend strongly on ω_(e).

[0091] The above results can be explained on simple physical grounds.When the ions rotate in the diamagnetic direction, the ions are confinedmagnetically by the Lorentz force. This was shown in FIG. 3A. Forelectrons, rotating in the same direction as the ions, the Lorentz forceis in the opposite direction, so that electrons would not be confined.The electrons leave the plasma and, as a result, a surplus of positivecharge is created. This sets up an electric field that prevents otherelectrons from leaving the plasma. The direction and the magnitude ofthis electric field, in equilibrium, is determined by the conservationof momentum.

[0092] The electrostatic field plays an essential role on the transportof both electrons and ions. Accordingly, an important aspect of thisinvention is that a strong electrostatic field is created inside theplasma layer 106, the magnitude of this electrostatic field iscontrolled by the value of the applied magnetic field Bo which can beeasily adjusted.

[0093] As explained, the electrostatic field is confining for electronsif ω_(e)>0. As shown in FIG. 10B, the depth of the well can be increasedby tuning the applied magnetic field B₀. Except for a very narrow regionnear the null circle, the electrons always have a small gyroradius.Therefore, electrons respond to short-wavelength fluctuations with ananomalously fast diffusion rate. This diffusion, in fact, helps maintainthe potential well once the fusion reaction occurs. The fusion productions, being of much higher energy, leave the plasma. To maintain chargequasi-neutrality, the fusion products must pull electrons out of theplasma with them, mainly taking the electrons from the surface of theplasma layer. The density of electrons at the surface of the plasma isvery low, and the electrons that leave the plasma with the fusionproducts must be replaced; otherwise, the potential well woulddisappear.

[0094]FIG. 11 shows a Maxwellian distribution 162 of electrons. Onlyvery energetic electrons from the tail 160 of the Maxwell distributioncan reach the surface of the plasma and leave with fusion ions. The tail160 of the distribution 162 is thus continuously created byelectron-electron collisions in the region of high density near the nullsurface. The energetic electrons still have a small gyroradius, so thatanomalous diffusion permits them to reach the surface fast enough toaccommodate the departing fusion product ions. The energetic electronslose their energy ascending the potential well and leave with verylittle energy. Although the electrons can cross the magnetic fieldrapidly, due to anomalous transport, anomalous energy losses tend to beavoided because little energy is transported.

[0095] Another consequence of the potential well is a strong coolingmechanism for electrons that is similar to evaporative cooling. Forexample, for water to evaporate, it must be supplied the latent heat ofvaporization. This heat is supplied by the remaining liquid water andthe surrounding medium, which then thermalize rapidly to a lowertemperature faster than the heat transport processes can replace theenergy. Similarly, for electrons, the potential well depth is equivalentto water's latent heat of vaporization. The electrons supply the energyrequired to ascend the potential well by the thermalization process thatre-supplies the energy of the Maxwell tail so that the electrons canescape. The thermalization process thus results in a lower electrontemperature, as it is much faster than any heating process. Because ofthe mass difference between electrons and protons, the energy transfertime from protons is about 1800 times less than the electronthermalization time. This cooling mechanism also reduces the radiationloss of electrons. This is particularly important for advanced fuels,where radiation losses are enhanced by fuel ions with an atomic number Zgreater than 1; Z>1.

[0096] The electrostatic field also affects ion transport. The majorityof particle orbits in the plasma layer 106 are betatron orbits 112.Large-angle collisions, that is, collisions with scattering anglesbetween 90° and 180°, can change a betatron orbit to a drift orbit. Asdescribed above, the direction of rotation of the drift orbit isdetermined by a competition between the {right arrow over (E)}×{rightarrow over (B)} drift and the gradient drift. If the {right arrow over(E)}×{right arrow over (B)} drift dominates, the drift orbit rotates inthe diamagnetic direction. If the gradient drift dominates, the driftorbit rotates in the counterdiamagnetic direction. This is shown inFIGS. 12A and 12B. FIG. 12A shows a transition from a betatron orbit toa drift orbit due to a 180° collision, which occurs at the point 172.The drift orbit continues to rotate in the diamagnetic direction becausethe {right arrow over (E)}×{right arrow over (B)} drift dominates. FIG.12B shows another 180° collision, but in this case the electrostaticfield is weak and the gradient drift dominates. The drift orbit thusrotates in the counterdiamagnetic direction.

[0097] The direction of rotation of the drift orbit determines whetherit is confined or not. A particle moving in a drift orbit will also havea velocity parallel to the FRC axis. The time it takes the particle togo from one end of the FRC to the other, as a result of its parallelmotion, is called transit time; thus, the drift orbits reach an end ofthe FRC in a time of the order of the transit time. As shown inconnection with FIG. 9A, the Lorentz force at the ends of the FRC isconfining only for drift orbits rotating in the diamagnetic direction.After a transit time, therefore, ions in drift orbits rotating in thecounterdiamagnetic direction are lost.

[0098] This phenomenon accounts for a loss mechanism for ions, which isexpected to have existed in all FRC experiments. In fact, in theseexperiments, the ions carried half of the current and the electronscarried the other half. In these conditions the electric field insidethe plasma was negligible, and the gradient drift always dominated the{right arrow over (E)}×{right arrow over (B)} drift. Hence, all thedrift orbits produced by large-angle collisions were lost after atransit time. These experiments reported ion diffusion rates that werefaster than those predicted by classical diffusion estimates.

[0099] If there is a strong electrostatic field, the {right arrow over(E)}×{right arrow over (B)} drift dominates the gradient drift, and thedrift orbits rotate in the diamagnetic direction. This was shown abovein connection with FIG. 12A. When these orbits reach the ends of theFRC, they are reflected back into the region of closed field lines bythe Lorentz force; thus, they remain confined in the system.

[0100] The electrostatic fields in the colliding beam system may bestrong enough, so that the {right arrow over (E)}×{right arrow over (B)}drift dominates the gradient drift. Thus, the electrostatic field of thesystem would avoid ion transport by eliminating this ion loss mechanism,which is similar to a loss cone in a mirror device.

[0101] Another aspect of ion diffusion can be appreciated by consideringthe effect of small-angle, electron-ion collisions on betatron orbits.FIG. 13A shows a betatron orbit 112; FIG. 13B shows the same orbit 112when small-angle electron-ion collisions are considered 174; FIG. 13Cshows the orbit of FIG. 13B followed for a time that is longer by afactor of ten 176; and FIG. 13D shows the orbit of FIG. 13B followed fora time longer by a factor of twenty 178. It can be seen that thetopology of betatron orbits does not change due to small-angle,electron-ion collisions; however, the amplitude of their radialoscillations grows with time. In fact, the orbits shown in FIGS. 13A to13D fatten out with time, which indicates classical diffusion.

[0102] Formation of the FRC

[0103] Conventional procedures used to form a FRC primarily employ thetheta pinch-field reversal procedure. In this conventional method, abias magnetic field is applied by external coils surrounding a neutralgas back-filled chamber. Once this has occurred, the gas is ionized andthe bias magnetic field is frozen in the plasma. Next, the current inthe external coils is rapidly reversed and the oppositely orientedmagnetic field lines connect with the previously frozen lines to formthe closed topology of the FRC (see FIG. 2). This formation process islargely empirical and there exists almost no means of controlling theformation of the FRC. The method has poor reproducibility and no tuningcapability as a result.

[0104] In contrast, the FRC formation methods of the present inventionallow for ample control and provide a much more transparent andreproducible process. In fact, the FRC formed by the methods of thepresent invention can be tuned and its shape as well as other propertiescan be directly influenced by manipulation of the magnetic field appliedby the outer field coils 325. Formation of the FRC by methods of thepresent inventions also results in the formation of the electric fieldand potential well in the manner described in detail above. Moreover,the present methods can be easily extended to accelerate the FRC toreactor level parameters and high-energy fuel currents, andadvantageously enables the classical confinement of the ions.Furthermore, the technique can be employed in a compact device and isvery robust as well as easy to implement—all highly desirablecharacteristics for reactor systems.

[0105] In the present methods, FRC formation relates to the circulatingplasma beam 335. It can be appreciated that the circulating plasma beam335, because it is a current, creates a poloidal magnetic field, aswould an electrical current in a circular wire. Inside the circulatingplasma beam 335, the magnetic self-field that it induces opposes theexternally applied magnetic field due to the outer coil 325. Outside theplasma beam 335, the magnetic self-field is in the same direction as theapplied magnetic field. When the plasma ion current is sufficientlylarge, the self-field overcomes the applied field, and the magneticfield reverses inside the circulating plasma beam 335, thereby formingthe FRC topology as shown in FIGS. 2 and 4.

[0106] The requirements for field reversal can be estimated with asimple model. Consider an electric current I_(P) carried by a ring ofmajor radius r₀ and minor radius a<<r₀. The magnetic field at the centerof the ring normal to the ring is B_(p)=2πI_(P)/(cr_(o)). Assume thatthe ring current I_(P)=N_(p)e(Ω₀/2π) is carried by N_(P) ions that havean angular velocity ω₀. For a single ion circulating at radius r₀=V₀/Ω₀,Ω₀=eB₀/m_(i)c is the cyclotron frequency for an external magnetic fieldB₀. Assume V₀ is the average velocity of the beam ions. Field reversalis defined as $\begin{matrix}{{B_{p} = {\frac{N_{p}e\quad \Omega_{0}}{r_{0}c} \geq {2B_{0}}}},} & (3)\end{matrix}$

[0107] which implies that N_(p)>2 r₀/α_(i), and $\begin{matrix}{{I_{p} \geq \frac{e\quad V_{0}}{\pi \quad \alpha_{i}}},} & (4)\end{matrix}$

[0108] where α_(i)=e²/m_(i)c²=1.57×10⁻¹⁶ cm and the ion beam energy is$\frac{1}{2}m_{i}{V_{0}^{2}.}$

[0109] In the one-dimensional model, the magnetic field from the plasmacurrent is B_(p)=(2π/c)i_(p), where i_(p) is current per unit of length.The field reversal requirement is i_(p)>eV₀/πr₀α_(i)=0.225 kA/cm, whereB₀=69.3 G and${\frac{1}{2}m_{i}V_{0}^{2}} = {100\quad e\quad {V.}}$

[0110] For a model with periodic rings and B_(z) is averaged over theaxial coordinate

B_(z)

=(2π/c)(I_(p)/s) (s is the ring spacing), if s=r₀, this model would havethe same average magnetic field as the one dimensional model withi_(p)=I_(p)/s.

[0111] Combined Beam/Betatron Formation Technique

[0112] A preferred method of forming a FRC within the confinement system300 described above is herein termed the combined beam/betatrontechnique. This approach combines low energy beams of plasma ions withbetatron acceleration using the betatron flux coil 320.

[0113] The first step in this method is to inject a substantiallyannular cloud layer of background plasma in the chamber 310 using thebackground plasma sources 345. Outer coil 325 produces a magnetic fieldinside the chamber 310, which magnetizes the background plasma. At shortintervals, low energy ion beams are injected into the chamber 310through the injector ports 340 substantially transverse to theexternally applied magnetic field within the chamber 310. As explainedabove, the ion beams are trapped within the chamber 310 in largebetatron orbits by this magnetic field. The ion beams may be generatedby an ion accelerator, such as an accelerator comprising an ion diodeand a Marx generator. (see R. B. Miller, An Introduction to the Physicsof Intense Charged Particle Beams, (1982)). As one of skill in the artcan appreciate, the externally applied magnetic field will exert aLorentz force on the injected ion beam as soon as it enters the chamber310; however, it is desired that the beam not deflect, and thus notenter a betatron orbit, until the ion beam reaches the circulatingplasma beam 335. To solve this problem, the ion beams are neutralizedwith electrons and directed through a substantially constantunidirectional magnetic field before entering the chamber 310. Asillustrated in FIG. 14, when the ion beam 350 is directed through anappropriate magnetic field, the positively charged ions and negativelycharged electrons separate. The ion beam 350 thus acquires an electricself-polarization due to the magnetic field. This magnetic field may beproduced by, e.g., a permanent magnet or by an electromagnet along thepath of the ion beam. When subsequently introduced into the confinementchamber 310, the resultant electric field balances the magnetic force onthe beam particles, allowing the ion beam to drift undeflected. FIG. 15shows a head-on view of the ion beam 350 as it contacts the plasma 335.As depicted, electrons from the plasma 335 travel along magnetic fieldlines into or out of the beam 350, which thereby drains the beam'selectric polarization. When the beam is no longer electricallypolarized, the beam joins the circulating plasma beam 335 in a betatronorbit around the principle axis 315, as shown in FIG. 1 (see also FIG.4).

[0114] When the plasma beam 335 travels in its betatron orbit, themoving ions comprise a current, which in turn gives rise to a poloidalmagnetic self-field. To produce the FRC topology within the chamber 310,it is necessary to increase the velocity of the plasma beam 335, thusincreasing the magnitude of the magnetic self-field that the plasma beam335 causes. When the magnetic self-field is large enough, the directionof the magnetic field at radial distances from the axis 315 within theplasma beam 335 reverses, giving rise to a FRC. (See FIGS. 2 and 4). Itcan be appreciated that, to maintain the radial distance of thecirculating plasma beam 335 in the betatron orbit, it is necessary toincrease the applied magnetic field from the outer coil 325 as theplasma beam 335 increases in velocity. A control system is thus providedfor maintaining an appropriate applied magnetic field, dictated by thecurrent through the outer coil 325. Alternatively, a second outer coilmay be used to provide the additional applied magnetic field that isrequired to maintain the radius of the plasma beam's orbit as it isaccelerated.

[0115] To increase the velocity of the circulating plasma beam 335 inits orbit, the betatron flux coil 320 is provided. Referring to FIG. 16,it can be appreciated that increasing a current through the betatronflux coil 320, by Ampere's Law, induces an azimuthal electric field, E,inside the chamber 310. The positively charged ions in the plasma beam335 are accelerated by this induced electric field, leading to fieldreversal as described above. When ion beams are added to the circulatingplasma beam 335, as described above, the plasma beam 335 depolarizes theion beams.

[0116] For field reversal, the circulating plasma beam 335 is preferablyaccelerated to a rotational energy of about 100 eV, and preferably in arange of about 75 eV to 125 eV. To reach fusion relevant conditions, thecirculating plasma beam 335 is preferably accelerated to about 200 keVand preferably to a range of about 100 keV to 3.3 MeV.

[0117] FRC formation was successfully demonstrated utilizing thecombined beam/betatron formation technique. The combined beam/betatronformation technique was performed experimentally in a chamber 1 m indiameter and 1.5 m in length using an externally applied magnetic fieldof up to 500 G, a magnetic field from the betatron flux coil 320 of upto 5 kG, and a vacuum of 1.2×10⁻⁵ torr. In the experiment, thebackground plasma had a density of 10¹³ cm⁻³ and the ion beam was aneutralized Hydrogen beam having a density of 1.2×10¹³ cm⁻³, a velocityof 2×10⁷ cm/s, and a pulse length of around 20 μs (at half height).Field reversal was observed.

[0118] Betatron Formation Technique

[0119] Another preferred method of forming a FRC within the confinementsystem 300 is herein termed the betatron formation technique. Thistechnique is based on driving the betatron induced current directly toaccelerate a circulating plasma beam 335 using the betatron flux coil320. A preferred embodiment of this technique uses the confinementsystem 300 depicted in FIG. 1, except that the injection of low energyion beams is not necessary.

[0120] As indicated, the main component in the betatron formationtechnique is the betatron flux coil 320 mounted in the center and alongthe axis of the chamber 310. Due to its separate parallel windingsconstruction, the coil 320 exhibits very low inductance and, whencoupled to an adequate power source, has a low LC time constant, whichenables rapid ramp up of the current in the flux coil 320.

[0121] Preferably, formation of the FRC commences by energizing theexternal field coils 325, 330. This provides an axial guide field aswell as radial magnetic field components near the ends to axiallyconfine the plasma injected into the chamber 310. Once sufficientmagnetic field is established, the background plasma sources 345 areenergized from their own power supplies. Plasma emanating from the gunsstreams along the axial guide field and spreads slightly due to itstemperature. As the plasma reaches the mid-plane of the chamber 310, acontinuous, axially extending, annular layer of cold, slowly movingplasma is established.

[0122] At this point the betatron flux coil 320 is energized. Therapidly rising current in the coil 320 causes a fast changing axial fluxin the coil's interior. By virtue of inductive effects this rapidincrease in axial flux causes the generation of an azimuthal electricfield E (see FIG. 17), which permeates the space around the flux coil.By Maxwell's equations, this electric field E is directly proportionalto the change in strength of the magnetic flux inside the coil, i.e.: afaster betatron coil current ramp-up will lead to a stronger electricfield.

[0123] The inductively created electric field E couples to the chargedparticles in the plasma and causes a ponderomotive force, whichaccelerates the particles in the annular plasma layer. Electrons, byvirtue of their smaller mass, are the first species to experienceacceleration. The initial current formed by this process is, thus,primarily due to electrons. However, sufficient acceleration time(around hundreds of micro-seconds) will eventually also lead to ioncurrent. Referring to FIG. 17, this electric field E accelerates theelectrons and ions in opposite directions. Once both species reach theirterminal velocities, current is carried about equally by ions andelectrons.

[0124] As noted above, the current carried by the rotating plasma givesrise to a self magnetic field. The creation of the actual FRC topologysets in when the self magnetic field created by the current in theplasma layer becomes comparable to the applied magnetic field from theexternal field coils 325, 330. At this point magnetic reconnectionoccurs and the open field lines of the initial externally producedmagnetic field begin to close and form the FRC flux surfaces (see FIGS.2 and 4).

[0125] The base FRC established by this method exhibits modest magneticfield and particle energies that are typically not at reactor relevantoperating parameters. However, the inductive electric acceleration fieldwill persist, as long as the current in the betatron flux coil 320continues to increase at a rapid rate. The effect of this process isthat the energy and total magnetic field strength of the FRC continuesto grow. The extent of this process is, thus, primarily limited by theflux coil power supply, as continued delivery of current requires amassive energy storage bank. However, it is, in principal,straightforward to accelerate the system to reactor relevant conditions.

[0126] For field reversal, the circulating plasma beam 335 is preferablyaccelerated to a rotational energy of about 100 eV, and preferably in arange of about 75 eV to 125 eV. To reach fusion relevant conditions, thecirculating plasma beam 335 is preferably accelerated to about 200 keVand preferably to a range of about 100 keV to 3.3 MeV. When ion beamsare added to the circulating plasma beam 335, as described above, theplasma beam 335 depolarizes the ion beams.

[0127] FRC formation utilizing the betatron formation technique wassuccessfully demonstrated at the following parameter levels:

[0128] Vacuum chamber dimensions: about 1 m diameter, 1.5 m length.

[0129] Betatron coil radius of 10 cm.

[0130] Plasma orbit radius of 20 cm.

[0131] Mean external magnetic field produced in the vacuum chamber wasup to 100 Gauss, with a ramp-up period of 150 μs and a mirror ratio of 2to 1. (Source: Outer coils and betatron coils).

[0132] The background plasma (substantially Hydrogen gas) wascharacterized by a mean density of about 10¹³ cm⁻³, kinetic temperatureof less than 10 eV.

[0133] The lifetime of the configuration was limited by the total energystored in the experiment and generally was around 30 μs.

[0134] The experiments proceeded by first injecting a background plasmalayer by two sets of coaxial cable guns mounted in a circular fashioninside the chamber. Each collection of 8 guns was mounted on one of thetwo mirror coil assemblies. The guns were azimuthally spaced in anequidistant fashion and offset relative to the other set. Thisarrangement allowed for the guns to be fired simultaneously and therebycreated an annular plasma layer.

[0135] Upon establishment of this layer, the betatron flux coil wasenergized. Rising current in the betatron coil windings caused anincrease in flux inside the coil, which gave rise to an azimuthalelectric field curling around the betatron coil. Quick ramp-up and highcurrent in the betatron flux coil produced a strong electric field,which accelerated the annular plasma layer and thereby induced asizeable current. Sufficiently strong plasma current produced a magneticself-field that altered the externally supplied field and caused thecreation of the field reversed configuration. Detailed measurements withB-dot loops identified the extent, strength and duration of the FRC.

[0136] An example of typical data is shown by the traces of B-dot probesignals in FIG. 18. The data curve A represents the absolute strength ofthe axial component of the magnetic field at the axial mid-plane (75 cmfrom either end plate) of the experimental chamber and at a radialposition of 15 cm. The data curve B represents the absolute strength ofthe axial component of the magnetic field at the chamber axial mid-planeand at a radial position of 30 cm. The curve A data set, therefore,indicates magnetic field strength inside of the fuel plasma layer(between betatron coil and plasma) while the curve B data set depictsthe magnetic field strength outside of the fuel plasma layer. The dataclearly indicates that the inner magnetic field reverses orientation (isnegative) between about 23 and 47 μs, while the outer field stayspositive, i.e., does not reverse orientation. The time of reversal islimited by the ramp-up of current in the betatron coil. Once peakcurrent is reached in the betatron coil, the induced current in the fuelplasma layer starts to decrease and the FRC rapidly decays. Up to nowthe lifetime of the FRC is limited by the energy that can be stored inthe experiment. As with the injection and trapping experiments, thesystem can be upgraded to provide longer FRC lifetime and accelerationto reactor relevant parameters.

[0137] Overall, this technique not only produces a compact FRC, but itis also robust and straightforward to implement. Most importantly, thebase FRC created by this method can be easily accelerated to any desiredlevel of rotational energy and magnetic field strength. This is crucialfor fusion applications and classical confinement of high-energy fuelbeams.

[0138] Fusion

[0139] Significantly, these two techniques for forming a FRC inside of acontainment system 300 described above, or the like, can result inplasmas having properties suitable for causing nuclear fusion therein.More particularly, the FRC formed by these methods can be accelerated toany desired level of rotational energy and magnetic field strength. Thisis crucial for fusion applications and classical confinement ofhigh-energy fuel beams. In the confinement system 300, therefore, itbecomes possible to trap and confine high-energy plasma beams forsufficient periods of time to cause a fusion reaction therewith.

[0140] To accommodate fusion, the FRC formed by these methods ispreferably accelerated to appropriate levels of rotational energy andmagnetic field strength by betatron acceleration. Fusion, however, tendsto require a particular set of physical conditions for any reaction totake place. In addition, to achieve efficient burn-up of the fuel andobtain a positive energy balance, the fuel has to be kept in this statesubstantially unchanged for prolonged periods of time. This isimportant, as high kinetic temperature and/or energy characterize afusion relevant state. Creation of this state, therefore, requiressizeable input of energy, which can only be recovered if most of thefuel undergoes fusion. As a consequence, the confinement time of thefuel has to be longer than its burn time. This leads to a positiveenergy balance and consequently net energy output.

[0141] A significant advantage of the present invention is that theconfinement system and plasma described herein are capable of longconfinement times, i.e., confinement times that exceed fuel burn times.A typical state for fusion is, thus, characterized by the followingphysical conditions (which tend to vary based on fuel and operatingmode):

[0142] Average ion temperature: in a range of about 30 to 230 keV andpreferably in a range of about 80 keV to 230 keV

[0143] Average electron temperature: in a range of about 30 to 100 keVand preferably in a range of about 80 to 100 keV

[0144] Coherent energy of the fuel beams (injected ion beams andcirculating plasma beam): in a range of about 100 keV to 3.3 MeV andpreferably in a range of about 300 keV to 3.3 MeV.

[0145] Total magnetic field: in a range of about 47.5 to 120 kG andpreferably in a range of about 95 to 120 kG (with the externally appliedfield in a range of about 2.5 to 15 kG and preferably in a range ofabout 5 to 15 kG).

[0146] Classical Confinement time: greater than the fuel burn time andpreferably in a range of about 10 to 100 seconds.

[0147] Fuel ion density: in a range of about 10¹⁴ to less than 10¹⁶ cm⁻³and preferably in a range of about 10¹⁴ to 10¹⁵ cm⁻³.

[0148] Total Fusion Power: preferably in a range of about 50 to 450kW/cm (power per cm of chamber length)

[0149] To accommodate the fusion state illustrated above, the FRC ispreferably accelerated to a level of coherent rotational energypreferably in a range of about 100 keV to 3.3 MeV, and more preferablyin a range of about 300 keV to 3.3 MeV, and a level of magnetic fieldstrength preferably in a range of about 45 to 120 kG, and morepreferably in a range of about 90 to 115 kG. At these levels, highenergy ion beams can be injected into the FRC and trapped to form aplasma beam layer wherein the plasma beam ions are magnetically confinedand the plasma beam electrons are electrostatically confined.

[0150] Preferably, the electron temperature is kept as low aspractically possible to reduce the amount of bremsstrahlung radiation,which can, otherwise, lead to radiative energy losses. The electrostaticenergy well of the present invention provides an effective means ofaccomplishing this.

[0151] The ion temperature is preferably kept at a level that providesfor efficient burn-up since the fusion cross-section is a function ofion temperature. High direct energy of the fuel ion beams is essentialto provide classical transport as discussed in this application. It alsominimizes the effects of instabilities on the fuel plasma. The magneticfield is consistent with the beam rotation energy. It is partiallycreated by the plasma beam (self-field) and in turn provides the supportand force to keep the plasma beam on the desired orbit.

[0152] Fusion Products

[0153] The fusion products are born in the power core predominantly nearthe null surface 86 from where they emerge by diffusion towards theseparatrix 84 (see FIGS. 2 and 4). This is due to collisions withelectrons (as collisions with ions do not change the center of mass andtherefore do not cause them to change field lines). Because of theirhigh kinetic energy (product ions have much higher energy than the fuelions), the fusion products can readily cross the separatrix 84. Oncethey are beyond the separatrix 84, they can leave along the open fieldlines 80 provided that they experience scattering from ion-ioncollisions. Although this collisional process does not lead todiffusion, it can change the direction of the ion velocity vector suchthat it points parallel to the magnetic field. These open field lines 80connect the FRC topology of the core with the uniform applied fieldprovided outside the FRC topology. Product ions emerge on differentfield lines, which they follow with a distribution of energies.Advantageously, the product ions and charge-neutralizing electronsemerge in the form of rotating annular beams from both ends of the fuelplasma. For example for a 50 MW design of a p-B¹¹ reaction, these beamswill have a radius of about 50 centimeters and a thickness of about 10centimeters. In the strong magnetic fields found outside the separatrix84 (typically around 100 kG), the product ions have an associateddistribution of gyro-radii that varies from a minimum value of about 1cm to a maximum of around 3 cm for the most energetic product ions.

[0154] Initially the product ions have longitudinal as well asrotational energy characterized by ½M(v_(par))² and ½M(V_(perp))².v_(perp) is the azimuthal velocity associated with rotation around afield line as the orbital center. Since the field lines spread out afterleaving the vicinity of the FRC topology, the rotational energy tends todecrease while the total energy remains constant. This is a consequenceof the adiabatic invariance of the magnetic moment of the product ions.It is well known in the art that charged particles orbiting in amagnetic field have a magnetic moment associated with their motion. Inthe case of particles moving along a slow changing magnetic field, therealso exists an adiabatic invariant of the motion described by½M(vperp)²/B. The product ions orbiting around their respective fieldlines have a magnetic moment and such an adiabatic invariant associatedwith their motion. Since B decreases by a factor of about 10 (indicatedby the spreading of the field lines), it follows that v_(perp) willlikewise decrease by about 3.2. Thus, by the time the product ionsarrive at the uniform field region their rotational energy would be lessthan 5% of their total energy; in other words almost all the energy isin the longitudinal component.

[0155] Energy Conversion

[0156] The direct energy conversion system of the present inventioncomprises an inverse cyclotron converter (ICC) 420 shown in FIGS. 19Aand 20A coupled to a (partially illustrated) power core 436 of acolliding beam fusion reactor (CBFR) 410 to form a plasma-electric powergeneration system 400. A second ICC (not shown) may be disposedsymmetrically to the left of the CBFR 410. A magnetic cusp 486 islocated between the CBFR 410 and the ICC 420 and is formed when the CBFR410 and ICC 420 magnetic fields merge.

[0157] Before describing the ICC 420 and its operation in detail, areview of a typical cyclotron accelerator is provided. In conventionalcyclotron accelerators, energetic ions with velocities perpendicular toa magnetic field rotate in circles. The orbit radius of the energeticions is determined by the magnetic field strength and theircharge-to-mass ratio, and increases with energy. However, the rotationfrequency of the ions is independent of their energy. This fact has beenexploited in the design of cyclotron accelerators.

[0158] Referring to FIG. 21A, a conventional cyclotron accelerator 700includes two mirror image C-shaped electrodes 710 forming mirror imageD-shaped cavities placed in a homogenous magnetic field 720 having fieldlines perpendicular to the electrodes' plane of symmetry, i.e., theplane of the page. An oscillating electric potential is applied betweenthe C-shaped electrodes (see FIG. 21B). Ions I are emitted from a sourceplaced in the center of the cyclotron 700. The magnetic field 720 isadjusted so that the rotation frequency of the ions matches that of theelectric potential and associated electric field. If an ion I crossesthe gap 730 between the C-shaped electrodes 710 in the same direction asthat of the electric field, it is accelerated. By accelerating the ionI, its energy and orbit radius increase. When the ion has traveled ahalf-circle arc (experiencing no increase in energy), it crosses the gap730 again. Now the electric field between the C-shaped electrodes 710has reversed direction. The ion I is again accelerated, and its energyis further increased. This process is repeated every time the ioncrosses the gap 730 provided its rotation frequency continues to matchthat of the oscillating electric field (see FIG. 21C). If on the otherhand a particle crosses the gap 730 when the electric field is in theopposite direction it will be decelerated and returned to the source atthe center. Only particles with initial velocities perpendicular to themagnetic field 720 and that cross the gaps 730 in the proper phase ofthe oscillating electric field will be accelerated. Thus, proper phasematching is essential for acceleration.

[0159] In principle, a cyclotron could be used to extract kinetic energyfrom a pencil beam of identical energetic ions. Deceleration of ionswith a cyclotron, but without energy extraction has been observed forprotons, as described by Bloch and Jeffries in Phys. Rev. 80, 305(1950). The ions could be injected into the cavity such that they arebrought into a decelerating phase relative to the oscillating field. Allof the ions would then reverse the trajectory T of the accelerating ionshown in FIG. 21A. As the ions slow down due to interaction with theelectric field, their kinetic energy is transformed into oscillatingelectric energy in the electric circuit of which the cyclotron is part.Direct conversion to electric energy would be achieved, tending to occurwith very high efficiency.

[0160] In practice, the ions of an ion beam would enter the cyclotronwith all possible phases. Unless the varying phases are compensated forin the design of the cyclotron, half of the of the ions would beaccelerated and the other half decelerated. As a result, the maximumconversion efficiency would effectively be 50%. Moreover the annularfusion product ion beams discussed above are of an unsuitable geometryfor the conventional cyclotron.

[0161] As discussed in greater detail below, the ICC of the presentinvention accommodates the annular character of the fusion product beamsexiting the FRC of fusion reactor power core, and the random relativephase of the ions within the beam and the spread of their energies.

[0162] Referring back to FIG. 19A, a portion of a power core 436 of theCBFR 410 is illustrated on the left side, wherein a plasma fuel core 435is confined in a FRC 470 formed in part due to a magnetic field appliedby outside field coils 425. The FRC 470 includes closed field lines 482,a separatrix 484 and open field lines 480, which, as noted above,determines the properties of the annular beam 437 of the fusionproducts. The open field lines 480 extend away from the power core 436towards the magnetic cusp 486. As noted above, fusion products emergefrom the power core 436 along open field lines 480 in the form of anannular beam 437 comprising energetic ions and charge neutralizingelectrons.

[0163] The geometry of the ICC 420 is like a hollow cylinder with alength of about five meters. Preferably, four or more equal,semi-cylindrical electrodes 494 with small, straight gaps 497 make upthe cylinder surface. In operation, an oscillating potential is appliedto the electrodes 494 in an alternating fashion. The electric field Ewithin the converter has a quadrupole structure as indicated in the endview illustrated in FIG. 19B. The electric field E vanishes on thesymmetry axis and increases linearly with the radius; the peak value isat the gap 497.

[0164] In addition, the ICC 420 includes outside field coils 488 to forma uniform field within the ICC's hollow cylinder geometry. Because thecurrent runs through the ICC field coils 488 in a direction opposite tothe direction of the current running through the CBFR field coils 425,the field lines 496 in the ICC 420 run in a direction opposite to thedirection of the open field lines 480 of the CBFR 410. At an endfurthest from the power core 436 of the CBFR 410, the ICC 420 includesan ion collector 492.

[0165] In between the CBFR 410 and the ICC 420 is a symmetric magneticcusp 486 wherein the open field lines 480 of the CBFR 410 merge with thefield lines 496 of the ICC 420. An annular shaped electron collector 490is position about the magnetic cusp 486 and electrically coupled to theion collector 498. As discussed below, the magnetic field of themagnetic cusps 486 converts the axial velocity of the beam 437 to arotational velocity with high efficiency. FIG. 19C illustrates a typicalion orbit 422 within the converter 420.

[0166] The CBFR 410 has a cylindrical symmetry. At its center is thefusion power core 436 with a fusion plasma core 435 contained in a FRC470 magnetic field topology in which the fusion reactions take place. Asnoted, the product nuclei and charge-neutralizing electrons emerge asannular beams 437 from both ends of the fuel plasma 435. For example fora 50 MW design of a p-B¹¹ reaction, these beams will have a radius ofabout 50 cm and a thickness of about 10 cm. The annular beam has adensity n≅10⁷-10⁸ cm³. For such a density, the magnetic cusp 486separates the electrons and ions. The electrons follow the magneticfield lines to the electron collector 490 and the ions pass through thecusp 486 where the ion trajectories are modified to follow asubstantially helical path along the length of the ICC 420. Energy isremoved from the ions as they spiral past the electrodes 494 connectedto a resonant circuit (not shown). The loss of perpendicular energy isgreatest for the highest energy ions that initially circulate close tothe electrodes 494, where the electric field is strongest.

[0167] The ions arrive at the magnetic cusp 486 with the rotationalenergy approximately equal to the initial total energy, i.e., ½Mv_(P)²≅½Mv₀ ². There is a distribution of ion energies and ion initial radiir₀ when the ions reach the magnetic cusp 486. However, the initial radiir₀ tends to be approximately proportional to the initial velocity v₀.The radial magnetic field and the radial beam velocity produce a Lorentzforce in the azimuthal direction. The magnetic field at the cusp 486does not change the particle energy but converts the initial axialvelocity v_(P)≅v₀ to a residual axial velocity v_(z) and an azimuthalvelocity v_(⊥), where v₀ ²=v_(z) ²+v_(⊥) ². The value of the azimuthalvelocity v_(⊥) can be determined from the conservation of canonicalmomentum $\begin{matrix}{P_{\theta} = {{{{Mr}_{0}v_{\bot}} - \frac{{qB}_{0}r_{0}^{2}}{2c}} = \frac{{qB}_{0}r_{0}^{2}}{2c}}} & (5)\end{matrix}$

[0168] A beam ion enters the left hand side of the cusp 486 withB_(z)=B₀, v_(z)=v₀, v_(⊥)=0 and r=r₀. It emerges on the right hand sideof the cusp 486 with r=r₀, B_(z)=−B₀, v_(⊥)=qB₀r₀/Mc and v_(z)={squareroot}{square root over (v₀ ²−v_(⊥) ²)} $\begin{matrix}{\frac{v_{z}}{v_{0}} = \sqrt{1 - \left( \frac{r_{0}\Omega_{0}}{v_{0}} \right)^{2}}} & (6)\end{matrix}$

[0169] where $\Omega_{0} = \frac{{qB}_{0}}{M\quad c}$

[0170] is the cyclotron frequency. The rotation frequency of the ions isin a range of about 1-10 MHz, and preferably in a of about 5-10 MHz,which is the frequency at which power generation takes place.

[0171] In order for the ions to pass through the cusp 486, the effectiveion gyro-radius must be greater than the width of the cusp 486 at theradius r₀. It is quite feasible experimentally to reduce the axialvelocity by a factor of 10 so that the residual axial energy will bereduced by a factor of 100. Then 99% of the ion energy will be convertedto rotational energy. The ion beam has a distribution of values for v₀and r₀. However, because r₀ is proportional to v₀ as previouslyindicated by the properties of the FRC based reactor, the conversionefficiency to rotational energy tends to be 99% for all ions.

[0172] As depicted in FIG. 19B, the symmetrical electrode structure ofthe ICC 420 of the present invention preferably includes four electrodes494. A tank circuit (not shown) is connected to the electrode structures494 so that the instantaneous voltages and electric fields are asillustrated. The voltage and the tank circuit oscillate at a frequencyof ω=Ω₀. The azimuthal electric field E at the gaps 497 is illustratedin FIG. 19B and FIG. 22. FIG. 22 illustrates the electric field in thegaps 497 between electrodes 494 and the field an ion experiences as itrotates with angular velocity ω₀. It is apparent that in a completerevolution the particle will experience alternately acceleration anddeceleration in an order determined by the initial phase. In addition tothe azimuthal electric field E_(θ) there is also a radial electric fieldE_(r). The azimuthal field E_(θ) is maximum in the gaps 497 anddecreases as the radius decreases. FIG. 22 assumes the particle rotatesmaintaining a constant radius. Because of the gradient in the electricfield the deceleration will always dominate over the acceleration. Theacceleration phase makes the ion radius increase so that when the ionnext encounters a decelerating electric field the ion radius will belarger. The deceleration phase will dominate independent of the initialphase of the ion because the radial gradient of the azimuthal electricfield E_(θ) is always positive. As a result, the energy conversionefficiency is not limited to 50% due to the initial phase problemassociated with conventional cyclotrons. The electric field E_(r) isalso important. It also oscillates and produces a net effect in theradial direction that returns the beam trajectory to the original radiuswith zero velocity in the plane perpendicular to the axis as in FIG.19C.

[0173] The process by which ions are always decelerated is similar tothe principle of strong focusing that is an essential feature of modemaccelerators as described in U.S. Pat. No. 2,736,799. The combination ofa positive (focusing) and negative lens (defocusing) is positive if themagnetic field has a positive gradient. A strong focusing quadrupoledoublet lens is illustrated in FIG. 23. The first lens is focusing inthe x-direction and defocusing in the y-direction. The second lens issimilar with x and y properties interchanged. The magnetic fieldvanishes on the axis of symmetry and has a positive radial gradient. Thenet results for an ion beam passing through both lenses is focusing inall directions independent of the order of passage.

[0174] Similar results have been reported for a beam passing through aresonant cavity containing a strong axial magnetic field and operatingin the TE₁₁₁ mode (see Yoshikawa et al.). This device is called apeniotron. In the TE₁₁₁ mode the resonant cavity has standing waves inwhich the electric field has quadrupole symmetry. The results arequalitatively similar to some of the results described herein. There arequantitative differences in that the resonance cavity is much larger insize (10 meter length), and operates at a much higher frequency (155MHz) and magnetic field (10 T). Energy extraction from the highfrequency waves requires a rectenna. The energy spectrum of the beamreduces the efficiency of conversion. The existence of two kinds of ionsis a more serious problem, but the efficiency of conversion is adequatefor a D-He³ reactor that produces 15 MeV protons.

[0175] A single particle orbit 422 for a particle within the ICC 420 isillustrated in FIG. 19C. This result was obtained by computer simulationand a similar result was obtained for the peniotron. An ion entering atsome radius r₀ spirals down the length of the ICC and after losing theinitial rotational energy converges to a point on a circle of the sameradius r₀. The initial conditions are asymmetric; the final statereflects this asymmetry, but it is independent of the initial phase sothat all particles are decelerated. The beam at the ion collector end ofthe ICC is again annular and of similar dimensions. The axial velocitywould be reduced by a factor of 10 and the density correspondinglyincreased. For a single particle an extracting efficiency of 99% isfeasible. However, various factors, such as perpendicular rotationalenergy of the annular beam before it enters the converter, may reducethis efficiency by about 5%. Electric power extraction would be at about1-10 MHz and preferably about 5-10 MHz, with additional reduction inconversion efficiency due to power conditioning to connect to a powergrid.

[0176] As shown in FIGS. 20A and 20B, alternative embodiments of theelectrode structures 494 in the ICC 420 may include two symmetricalsemi-circular electrodes and/or tapered electrodes 494 that tapertowards the ion collector 492.

[0177] Adjustments to the ion dynamics inside the main magnetic field ofthe ICC 420 may be implemented using two auxiliary coil sets 500 and510, as shown in FIGS. 24A and 24B. Both coil sets 500 and 510 involveadjacent conductors with oppositely directed currents, so the magneticfields have a short range. A magnetic-field gradient, as schematicallyillustrated in FIG. 24A, will change the ion rotation frequency andphase. A multi-pole magnetic field, as schematically illustrated in FIG.24B, will produce bunching, as in a linear accelerator.

[0178] Reactor

[0179]FIG. 25 illustrates a 100 MW reactor. The generator cut awayillustrates a fusion power core region having superconducting coils toapply a uniform magnetic field and a flux coil for formation of amagnetic field with field-reversed topology. Adjacent opposing ends ofthe fusion power core region are ICC energy converters for directconversion of the kinetic energy of the fusion products to electricpower. The support equipment for such a reactor is illustrated in FIG.26.

[0180] Propulsion System

[0181]FIG. 27 illustrates a plasma-thrust propulsion system 800. Thesystem includes a FRC power core 836 in which a fusion fuel core 835 iscontained and from both ends of which fusion products emerge in the formof an annular beam 837. An ICC energy converter 820 coupled to one endof the power core. A magnetic nozzle 850 is positioned adjacent theother end of the power core. The annular beam 837 of fusion productsstream from one end of the fusion power core along field lines into theICC for energy conversion and from the other end of the power core alongfield lines out of the nozzle for thrust T.

[0182] While the invention is susceptible to various modifications andalternative forms, a specific example thereof has been shown in thedrawings and is herein described in detail. It should be understood,however, that the invention is not to be limited to the particular formdisclosed, but to the contrary, the invention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the appended claims.

What is claimed is:
 1. An inverse cyclotron energy converter comprisinga cylindrical vessel, four or more semi-cylindrical electrodes forming acylindrical surface of the vessel and in spaced relation to form a gapbetween adjacent electrodes, first and second magnetic field generators,an electron collector interposing the first and second magnetic fieldgenerators and adjacent a first end of the four or more electrodes, andan ion collector positioned adjacent a second end of the four or moreelectrodes.
 2. The converter of claim 1 further comprising a resonantcircuit coupled to the four or more electrodes.
 3. The converter ofclaim 1 further comprising a tank circuit coupled to the four or moreelectrodes.
 4. The converter of claim 1 wherein the electron collectoris annularly shaped.
 5. The converter of claim 1 wherein the first andsecond magnetic field generators comprise annular field coils disposedabout the vessel, wherein the field lines of the magnetic fieldgenerated by the field coils of the first magnetic field generator runin a direction opposite to the field lines of the magnetic fieldgenerated by the field coils of the second magnetic field generator. 6.The converter of claim 1 wherein the electron collector and ioncollector are electrically coupled.
 7. The converter of claim 1 whereinthe four or more electrodes are symmetrical.
 8. A direct energyconverter comprising an enclosure, a means for forming a multipoleelectric field having three or more poles disposed within the enclosure,and a means for forming a magnetic cusp coupled to the vessel,
 9. Theconverter of claim 8 wherein the means for forming the electric fieldcomprises a plurality of electrodes.
 10. The converter of claim 9wherein the plurality of electrodes are symmetrical.
 11. The converterof claim 9 wherein the plurality of electrodes are semi-cylindrical. 12.The converter of claim 9 wherein the plurality of electrodes are inspaced relation with one another forming a gap between adjacentelectrodes.
 13. The converter of claim 8 wherein the plurality ofelectrodes includes at least 4 electrodes.
 14. The converter of claim 8wherein the means for forming a magnetic cusp comprises first and secondsets of field coils disposed about the enclosure.
 15. The converter ofclaim 14 wherein the first and second magnetic fields generated by thefirst and second sets of field coils have oppositely running fieldlines.
 16. The converter of claim 15 further comprising an electroncollector disposed a magnetic cusp region adjacent a first end of themeans for forming the multipole electric field.
 17. The converter ofclaim 16 wherein the electron collector is annularly shaped.
 18. Theconverter of claim 16 further comprising a ion collector disposedadjacent a second end of the means for forming the multi-pole electricfield.
 19. The converter of claim 18 wherein the ion collector isdisposed within the vessel.
 20. The converter of claim 8 furthercomprising a resonant circuit coupled to the means for forming amulti-pole electric field.
 21. The converter of claim 8 furthercomprising a tank circuit coupled to the means for forming a multi-poleelectric field.
 22. The converter of claim 18 wherein the electroncollector and ion collector are electrically coupled.
 23. An inversecyclotron energy converter comprising a plurality of electrodes forminga generally cylindrical cavity, the electrodes being in spaced relationforming a plurality of elongate gaps there between, wherein theplurality of electrodes comprises more than two electrodes, a magneticfield generator extending about the plurality of electrodes, and an ioncollector positioned at one end of the plurality of electrodes.
 24. Theconverter of claim 23 further comprising an electron collectorpositioned adjacent another end of the plurality of electrodes.
 25. Theconverter of claim 24 wherein the electron collector is annular inshape.
 26. The converter of claim 24 wherein the electron collector andion collector are electrically coupled.
 27. The converter of claim 23further comprising a tank circuit coupled to the plurality ofelectrodes.
 28. The converter of claim 23 wherein the magnetic fieldgenerator comprises a plurality of field coils extending about theplurality of electrodes.
 29. The converter of claim 23 wherein theplurality of electrodes are symmetrical.
 30. An inverse cyclotron energyconverter comprising at least four quadra-cylindrical electrodes formingan elongate cavity, the electrodes being in spaced relation forming atleast four elongate gaps there between, and a magnetic field generatorextending about the at least four electrodes.
 31. The converter of claim30 further comprising an ion collector positioned at a first end of theat least four electrodes, and an annular shaped electron collectorpositioned adjacent a second end of the at least four electrodes, theelectron and ion collectors being electrically coupled to one another.32. The converter of claim 30 further comprising a tank circuit coupledto the at least four electrodes.
 34. The converter of claim 30 whereinthe magnetic field generator comprises a plurality of field coilsextending about the at least four electrodes.